Rockfish Historical Harvest Estimates

Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest and releases of rockfish in Alaska waters and expand the time series back to 1977 when the statewide harvest survey (SWHS) was first implemented. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and replaces the Howard decision tree approach to low sample sizes with a hierarchical model. The methods and results for generating harvest estimates are generally consistent between the Bayesian model and the Howard methods. Harvest estimates are consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data.

The Bayesian methods depart from the Howard method in how releases are estimated. The Howard methods assume that the species composition of the harvests are equal to the species composition of released fish, which is clearly contraindicated in the logbook data. For instance, logbook data demonstrates that yelloweye have been retained at high levels up until restrictions were enacted in recent years, whereas pelagic rockfish were released in significant numbers in the past with retention increasing in recent years as they have become more prized by anglers. Recent prohibition on retaining yelloweye in Southeast Alaska highlights the the shortcomings of the original Howard methods as the species composition of the harvest would indicate that no yelloweye were caught and released during the closure. The Howard method for estimating releases for private anglers also relied on an expansion of the logbook release estimates based on the ratio of private:guided releases of all rockfish in the SWHS. In addition to the faulty assumptions about species composition, this method ignores potential bias in SWHS estimates of harvests and releases. As demonstrated below, the bias in those two quantities appears to be quite different based on the logbook data. The Bayesian model thus attempts to estimate release probabilities based on the logbook data coupled with bias corrected estimates from the SWHS.

Lastly, the Howard methods were only used on data beginning in 1999 with the advent of the logbook program and estimates of harvests and releases prior to that have been based on linear ramps from 1999 back to the perceived start of the fishery. The Bayesian methods allow us to expand the time series back to 1977 when the SWHS was implemented by leveraging regional data trends in species composition and the proportion of caught rockfish harvested by species and/or species complex. Key advantages of the Bayesian approach are highlighted in table 1.

Table 1. Summary of key improvements in reconstructiing sport fish removals of rockfish using the Bayesian model as compared to the Howard et al. (2020) methods.

Issue	Howard	Bayes
Time series	1999 - present	1977 - present
Bias in SWHS	Not explicitly dealt with. Relies on logbook data and ratios of guided/unguided from SWHS data to estimate unguided releases and harvests.	Explicitly estimates bias in SWHS harvest and release estimates based on logbook data.
Species composition of releases	Assumes that species composition of releases is equal to that of the harvest, which is not evident in the logbook data.	Recognizes different release probabilities by species / species assemblage and estimates it from logbook data and bias corrected SWHS data
Sample size limitations	Uses sample size threshholds such that when areas fall below those threshholds values are borrowed from nearby areas.	Uses a hierarchichacal modelling approach that shares information between areas in the same region. Thus all data is used, even with small sample sizes. This is a more sound method that avoids assumptions and uses all of the data.
Error propogation	Error is propogated when variance estimates are available, but there is uncertainty associated with borrowing values from nearby areas, or the assumption of species compositions being identical in harvest and releases, are not dealt with.	By breaking the assumption that species composition is equal between harvests and releases, uncertainty in the release estimates is more reflective of the fishery. Furthermore, the hyerarchichal approach more accurately captures uncertainy within and between areas within a region.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are overall harvest estimates from 1977- 1995 and release estimates from 1990-1995 that required some partitioning to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied to the pre-1996 values.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook records are a census of guided harvests and releases.

SWHS Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides have been required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

Figure 1.- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).

A note on model development

To evaluate the discrepancy in apparent bias in harvest and release data, several models were explored to estimate releases during model development. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treated the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases. This tensions eventually highlighted the different release/retention probabilities between yelloweye and pelagics in the logbook data and prompted the current approach whereby that probability was calculated for the three main species complexes covered in the data: pelagics, yelloweye, and “other”. The methods described here follow the (\(LB_{fit}\)) formulation. Based on model behavior it is unlikely that the (\(LB_{cens}\)) model would work as there would not be enough data to estimate release probabilities. However, it may be worth running the (\(LB_{hyb}\)) approach as a sensitivity test at the very least.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish. In Southeast Alaska, the number of Demersal Shelf Rockfish (DSR, of which yelloweye are one species) and slope rockfish are also recorded.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta0_{(comp)ayu} + \frac{\beta1_{(comp)ayu}}{(1 + exp(\beta2_{(comp)ayu}*(y - \beta3_{(comp)ayu})))} + \beta4_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior. \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernible change in composition over the observed time period. \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was used for hindcasting.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested, \(pH_{(comp)ayu}\), by area, year, user group and species grouping. Because release data from the SWHS is for all rockfish and the release data from logbooks is only subdivided into pelagics, yelloweye and “other” (non-pelagic, non-yelloweye), we only estimated \(pH_{(comp)ayu}\) for those categories. Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases. For non-yelloweye DSR and Slope rockfish assemblages in Southeast Alaska \(R_{(DSR)ayu}\) and \(R_{(slope)ayu}\) were estimated from \(R_{(other)ayu}\) using the species composition data from the harvest, thus assuming that slope and DSR assemblages were caught and released at the same rates.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta0_{(pH)ayu} + \frac{\beta1_{(pH)ayuc}}{(1 + exp(\beta2_{(pH)ayuc}*(y - \beta3_{(pH)ayuc})))} + \beta4_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990. As with the compositional trends, \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernable change in harvest probability over the observed time period, \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was applied.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. As such, the release data are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), a second approaches was considered that loosened the assumption that logbook releases were a census. Methods explored to develope \(LB_{hyb}\) and \(LB_{cens}\) models are detailed at the end of this section.

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs was thus a proportion of the pelagic harvests

\[\begin{equation} x_{(black)ayu}~\sim~\textrm{Binomial}(P_{(black)ayu}, N_{ayu}^{pel}) \end{equation}\]

Yelloweye rockfish in Southcentral and Kodiak were modeled similarly as a proportion of the total number of non-pelagics such that

\[\begin{equation} x_{(yellow_{R2})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R2})ayu}, N_{ayu}^{nonpel}) \end{equation}\]

Southeast areas have several other non-pelagic groupings such that DSR and slope rockfish are a proportion of non-pelagics

\[\begin{equation} x_{(DSR)ayu}~\sim~\textrm{Binomial}(P_{(DSR)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

and

\[\begin{equation} x_{(slope)ayu}~\sim~\textrm{Binomial}(P_{(slope)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

with yelloweye in southeast a proportion of the DSR harvest

\[\begin{equation} x_{(yellow_{R1})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R1})ayu}, N_{ayu}^{DSR}) \end{equation}\].

Alternative likelihoods for release estimates

To loosen the assumption that logbook release data are an effective census of true releases I explored models that treated logbook release estimates as a lower bound on the estimate of true releases. In a hybrid approach yelloweye and non-pelagic releases are regarded as a reliable census (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates (where censoring implies NA values) such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

This model formulation failed such that there was not enough data to inform pelagic releases and the values did not seem valid. A second approach is being explored that fits the censored data using a lognormal distribution centered around the logbook release value, but also with a lower bound equal to the number of recorded releases such that

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Logbook data is assumed to be a census and as such there is no estimate of uncertainty. As of this writing, several methods are being examined for how to treat \(\sigma_{Ray1}^2\). Models are being run that attempt to allow the model to estimate \(\sigma_{Ray1}^2\) with priors. A simple model applies a uniform prior (0.1,50) to \(\sigma_{Ray1}^2\). A hierarchichal approach based on regions is also being examined whereby \(\sigma_{Ray1}^2\) is lognormally distributed around hyper priors \(\mu_{\sigma_R}\) and \(\sigma_{\sigma_R}\). Initial efforts have applied a uniform prior on \(\mu_{\sigma_R}\) between 1 and 50 and on \(\sigma_{\sigma_R}\) between 0 and 10.

Priors.

Priors range from uninformative to very informative or fixed. Priors for compositional logistic parameters are in Table 2 and proportion harvest logistic parameters are in Table 3. Until I figure out how to make a nice table in Rmarkdown, please refer to the attached spreadsheet and comp and harvp tabs.

Unresolved issues and outstanding questions:

1. Reliability of unguided release estimates: These estimates have the least information feeding them and rely on the bias-corrected SWHS release estimates of all rockfish and the trends in release probability evident in the logbook data. The \(\beta4\) term that estimates the guided/unguided effect was given a very informative prior that tied the release probability of private anglers tightly to that of the charter fleet. The model is then trying to balance the three species complex estimates (pelagic, yelloweye and other) so that they sum to the total unguided releases estimated from the bias corrected SWHS data. For the most part this seems reasonable and appears to work, but there are certain areas where the estimates are “wonky”:

   1. Total rockfish releases more or less align with the total releases estimated with the Howard methods. Presumably, much of the discrepancy results from the substantial bias in release estimates from the SWHS. Interestingly, the logbook data indicates that the SWHS underestimates harvests but overestimates releases by a significant factor (Figure 23 and 24 below).
   2. In general, release estimates of black rockfish are substantially lower than those calculated using the Howard methods. Presumably, much of this derives from the bias correction of the SWHS release estimates.
   3. Yelloweye release estimates also differ considerably from the Howard estimates, but unlike black rockfish are sometimes lower and sometimes higher. Two areas in particular are a little head scratching. Yelloweye releases in the Kodiak Northeast area in particular are significantly lower than for guided anglers with the same pattern evident in Cook Inlet to a lesser extent. Cook Inlet yelloweye numbers are very small, so this is a sample size issue with little consequence. The cause of the Kodiak northeast estimates is not clear to me at this point, but the model estimates the proportion harvested by unguided anglers to be much lower than that of guided anglers, even with the informative prior on \(\beta4\). This must be a product of the bias corrected SWHS release estimates and how the model is partitioning that estimate into the 3 species complexes, but itis a bit a of head scratcher.

2. Proportion guided estimates: There is not much data on this proportion prior to 2011 and it is not modeled with any sort of trend as was done for species composition and harvest proportions. With the exception of Cook Inlet and North Gulf Coast areas, there is little, if any, trend apparent in the data and perhaps this approach is the best available given the data available. However, if there are data sources somewhere that could inform this part of the model they could be incorporated.

3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.

4. Proportion harvest estimates for non-pelagic, non-yelloweye in Kodiak WKMA: I need to adjust the prior on the inflection point, \(\beta3\), so that it is forced to occur after 2006. Right now the model is estimating inflection in two Kodiak areas before that point where there is no data to justify a shift. The current inflection is a result of the hierachichal model.

5. Proportion pelagic in PWS and CSEO: The parameters for these particular proportions are very slow to converge. For the CSEO, the estimates of the \(\beta\) parameters are similar to the other Southeast areas, but the mixing is poor over the length of the chains. In this case I think they will ultimately converge with a very long model run and the shape of the curve in the model output looks acceptable. For the two PWS areas the model seems to struggle with the disparate proportional data from the logbook and the port sampling. There is some wandering in the chains of the \(\beta0\) and \(\beta1\) terms and spikiness in the \(\beta2\) terms. I’ve been working on constraining the hyperpriors for PWS \(beta2\). Similar to CSEO, it may just entail a very long model run to reach convergence, but the shape of the curves looks reasonable.

Next steps:

Once the model is finalized, harvest and release numbers need to be converted into biomass removals. This is a two step process where release mortality estimates are applied to the release estimates to estimate the number of released rockfish that do not survive. This is based on studies and will reflect the values that the department has been using with the Howard methods. Region 2 (both Southcentral and Kodiak) have release-at-depth estimates from a number of years that they apply across all years and then calculate mortality rates based on those estiates. Southease does not have release-at-depth data and simply applies an assumed rate based on research.

Once release mortality is calculated average weight data is applied to convert numbers to biomass. The plan is to incorporate all of this into the model to propogate uncertainty into the posteriors. However, the model already takes a long time to run and I may explore a simpler approach using the posteriors from the numbers model to speed up processing.

Results

• Model: LB_fit_3pH

• Model Run: HR_fitLBR_2bias_hierPcomp_3pH_CLEAN_thru2023_5e+06_2025-03-30 (Naming convention: modelname_thruYEAR_iters_rundate)

• Proportion of parmaters converged (Rhat <= 1.1): 0.996

• See end of document for summary of unconverged parameters.

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

And black rockfish releases…

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 8.- DSR rockfish (including yelloweye) harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 9.- DSR rockfish releases (including yelloweye) 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 10.- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 11.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

Figure 12.- Residuals from logbook harvests

SWHS residuals

Figure 13.- Residuals from SWHS harvests.

Figure 14.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

Figure 15.- Mean percent of harvest by charter anglers.

When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although the model smooths out the changes and we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

Figure 16.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.

Figure 18.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 19.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 20.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

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SWHS bias

Figure 23 shows the mean estimate for SWHS bias in harvests and releases. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias. Bias in release estimates is substantial and whereas the SWHS appears to underestimate harvests, it appears to greatly overestimates releases by a factor of 2 or more in most areas as derived from logbook reported releases.

Figure 23.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

Our estimates of SWHS harvest bias track observations fairly well when he have guided harvest estimates. The estimates of release bias in the SWHS data track observed patterns to an extent, but appear to smooth these more volatile disagreements with the logbook data. Adam postulated in his initial start on this that some of this could be the result of the estimates of the proportion guided. This value was not modelled with a trend and thus applies a constant estimate when hindcasting. Data on these relationships could greatly improve this model.

Figure 24.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 25 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

Figure 25.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment. For the most part, P(black|pelagic) is relatively constant across areas, with the exception of Cook Inlet and NSEI in Southeast AK. It may be worth discussing whether the shifts in those areas is a result of improved or changing species identification rather than actual shift in the species composition of the catch.

Figure 26.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

Figure 27.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

Figure 28.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

Figure 30.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(slope|non-pelagic & non-yellowye) For release estimates

Figure 31.- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.

Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.

parameter n badRhat_avg beta0_pelagic 3 1.357379 beta1_pelagic 3 1.347707 beta1_pH 3 1.224399 beta2_pelagic 3 1.214859

parameter n badRhat_avg beta2_pH 2 1.207336 beta1_black 1 1.139553 beta2_yellow 1 1.133887 beta4_yellow 1 1.112259

Table 2. Summary of unconverged parameters by area

	BSAI	CI	CSEO	NSEI	NSEO	PWSI	PWSO	WKMA
beta0_pelagic	0	0	1	0	0	1	1	0
beta1_black	0	0	0	1	0	0	0	0
beta1_pelagic	0	0	1	0	0	1	1	0
beta1_pH	1	1	0	0	0	0	1	0
beta2_pelagic	0	0	1	0	1	1	0	0
beta2_pH	0	1	0	0	0	0	0	1
beta2_yellow	0	0	0	0	0	0	1	0
beta4_yellow	1	0	0	0	0	0	0	0

Parameter estimates:

Summary Table of Parameter Estimates

Parameter	mean	sd	Lower_CI	Median	Upper_CI
mu_bc_H[1]	-0.132	0.068	-0.259	-0.136	0.009
mu_bc_H[2]	-0.094	0.046	-0.172	-0.099	0.011
mu_bc_H[3]	-0.434	0.071	-0.568	-0.434	-0.288
mu_bc_H[4]	-0.986	0.189	-1.367	-0.983	-0.627
mu_bc_H[5]	0.938	0.966	-0.118	0.746	3.371
mu_bc_H[6]	-2.173	0.320	-2.809	-2.179	-1.516
mu_bc_H[7]	-0.443	0.109	-0.666	-0.440	-0.242
mu_bc_H[8]	0.240	0.356	-0.352	0.203	1.045
mu_bc_H[9]	-0.296	0.133	-0.554	-0.298	-0.027
mu_bc_H[10]	-0.104	0.071	-0.235	-0.105	0.044
mu_bc_H[11]	-0.122	0.037	-0.196	-0.122	-0.050
mu_bc_H[12]	-0.254	0.106	-0.484	-0.250	-0.057
mu_bc_H[13]	-0.135	0.077	-0.281	-0.136	0.020
mu_bc_H[14]	-0.303	0.096	-0.498	-0.301	-0.124
mu_bc_H[15]	-0.343	0.051	-0.442	-0.343	-0.242
mu_bc_H[16]	-0.258	0.369	-0.914	-0.282	0.511
mu_bc_R[1]	1.331	0.140	1.059	1.326	1.606
mu_bc_R[2]	1.450	0.092	1.262	1.452	1.629
mu_bc_R[3]	1.398	0.140	1.113	1.402	1.666
mu_bc_R[4]	0.896	0.203	0.454	0.908	1.264
mu_bc_R[5]	1.188	0.471	0.248	1.191	2.132
mu_bc_R[6]	-1.587	0.425	-2.457	-1.582	-0.769
mu_bc_R[7]	0.373	0.193	-0.018	0.378	0.744
mu_bc_R[8]	0.555	0.189	0.180	0.561	0.906
mu_bc_R[9]	0.340	0.205	-0.112	0.358	0.703
mu_bc_R[10]	1.294	0.135	1.023	1.297	1.545
mu_bc_R[11]	1.038	0.098	0.851	1.038	1.231
mu_bc_R[12]	0.812	0.202	0.416	0.812	1.204
mu_bc_R[13]	1.030	0.103	0.822	1.029	1.223
mu_bc_R[14]	0.896	0.145	0.609	0.896	1.167
mu_bc_R[15]	0.779	0.108	0.568	0.778	0.994
mu_bc_R[16]	1.091	0.126	0.836	1.093	1.340
tau_pH[1]	5.237	0.445	4.411	5.214	6.162
tau_pH[2]	2.059	0.222	1.653	2.044	2.519
tau_pH[3]	1.923	0.186	1.575	1.913	2.314
beta0_pH[1,1]	0.498	0.168	0.161	0.499	0.812
beta0_pH[2,1]	1.368	0.181	0.993	1.376	1.691
beta0_pH[3,1]	1.418	0.194	0.984	1.433	1.753
beta0_pH[4,1]	1.550	0.224	1.045	1.566	1.929
beta0_pH[5,1]	-0.856	0.271	-1.442	-0.843	-0.362
beta0_pH[6,1]	-0.700	0.498	-1.788	-0.618	-0.066
beta0_pH[7,1]	-0.483	0.461	-1.618	-0.453	0.380
beta0_pH[8,1]	-0.674	0.285	-1.347	-0.638	-0.220
beta0_pH[9,1]	-0.653	0.282	-1.257	-0.631	-0.177
beta0_pH[10,1]	0.231	0.203	-0.198	0.240	0.610
beta0_pH[11,1]	-0.095	0.171	-0.451	-0.087	0.221
beta0_pH[12,1]	0.487	0.189	0.113	0.487	0.856
beta0_pH[13,1]	0.008	0.146	-0.276	0.008	0.292
beta0_pH[14,1]	-0.314	0.166	-0.640	-0.315	0.003
beta0_pH[15,1]	-0.032	0.180	-0.397	-0.032	0.321
beta0_pH[16,1]	-0.511	0.399	-1.477	-0.430	0.049
beta0_pH[1,2]	2.819	0.167	2.471	2.823	3.127
beta0_pH[2,2]	2.881	0.134	2.612	2.882	3.145
beta0_pH[3,2]	3.121	0.170	2.797	3.126	3.438
beta0_pH[4,2]	2.950	0.135	2.684	2.949	3.218
beta0_pH[5,2]	4.721	1.360	2.990	4.439	8.332
beta0_pH[6,2]	3.121	0.204	2.731	3.120	3.523
beta0_pH[7,2]	1.961	0.171	1.615	1.959	2.296
beta0_pH[8,2]	2.872	0.170	2.555	2.867	3.217
beta0_pH[9,2]	3.435	0.217	3.013	3.427	3.869
beta0_pH[10,2]	3.744	0.197	3.349	3.741	4.127
beta0_pH[11,2]	-4.855	0.309	-5.495	-4.851	-4.264
beta0_pH[12,2]	-4.778	0.395	-5.556	-4.770	-4.010
beta0_pH[13,2]	-4.594	0.407	-5.339	-4.600	-3.760
beta0_pH[14,2]	-5.633	0.485	-6.636	-5.615	-4.755
beta0_pH[15,2]	-4.280	0.341	-4.941	-4.283	-3.603
beta0_pH[16,2]	-4.871	0.390	-5.697	-4.856	-4.137
beta0_pH[1,3]	1.900	0.180	1.542	1.899	2.252
beta0_pH[2,3]	2.219	0.164	1.892	2.218	2.542
beta0_pH[3,3]	2.527	0.154	2.225	2.525	2.827
beta0_pH[4,3]	2.934	0.175	2.582	2.936	3.266
beta0_pH[5,3]	2.308	1.624	0.068	1.989	6.391
beta0_pH[6,3]	0.036	0.970	-1.476	-0.154	1.747
beta0_pH[7,3]	-1.630	0.419	-2.493	-1.618	-0.831
beta0_pH[8,3]	0.303	0.201	-0.091	0.301	0.703
beta0_pH[9,3]	-0.824	0.548	-2.318	-0.712	-0.097
beta0_pH[10,3]	0.420	0.415	-0.578	0.471	1.083
beta0_pH[11,3]	-0.142	0.347	-0.793	-0.148	0.551
beta0_pH[12,3]	-0.809	0.351	-1.555	-0.776	-0.200
beta0_pH[13,3]	-0.147	0.322	-0.771	-0.143	0.460
beta0_pH[14,3]	-0.267	0.271	-0.801	-0.266	0.262
beta0_pH[15,3]	-0.681	0.308	-1.301	-0.666	-0.131
beta0_pH[16,3]	-0.385	0.293	-0.979	-0.385	0.197
beta1_pH[1,1]	3.148	0.310	2.588	3.132	3.784
beta1_pH[2,1]	2.153	0.275	1.677	2.128	2.746
beta1_pH[3,1]	1.981	0.311	1.476	1.957	2.676
beta1_pH[4,1]	2.416	0.367	1.859	2.366	3.269
beta1_pH[5,1]	2.280	0.329	1.719	2.257	3.015
beta1_pH[6,1]	3.894	1.150	2.333	3.668	6.725
beta1_pH[7,1]	2.654	0.912	1.036	2.558	4.923
beta1_pH[8,1]	4.092	1.064	2.631	3.830	6.631
beta1_pH[9,1]	2.341	0.393	1.725	2.295	3.231
beta1_pH[10,1]	2.396	0.280	1.887	2.376	3.011
beta1_pH[11,1]	3.276	0.218	2.882	3.267	3.712
beta1_pH[12,1]	2.547	0.223	2.121	2.548	2.988
beta1_pH[13,1]	2.967	0.216	2.561	2.963	3.408
beta1_pH[14,1]	3.420	0.213	3.004	3.417	3.851
beta1_pH[15,1]	2.532	0.227	2.096	2.526	2.985
beta1_pH[16,1]	4.192	0.747	3.202	4.046	5.981
beta1_pH[1,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[2,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[3,2]	0.020	0.146	0.000	0.000	0.022
beta1_pH[4,2]	0.004	0.105	0.000	0.000	0.003
beta1_pH[5,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[6,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[7,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[8,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[9,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[10,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[11,2]	6.702	0.340	6.053	6.690	7.390
beta1_pH[12,2]	6.447	0.469	5.584	6.433	7.430
beta1_pH[13,2]	6.976	0.442	6.080	6.979	7.829
beta1_pH[14,2]	7.286	0.504	6.336	7.273	8.348
beta1_pH[15,2]	6.763	0.375	6.036	6.773	7.496
beta1_pH[16,2]	7.471	0.426	6.673	7.456	8.351
beta1_pH[1,3]	0.002	0.010	0.000	0.000	0.025
beta1_pH[2,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[3,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[4,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[5,3]	3.457	7.899	1.358	2.749	6.816
beta1_pH[6,3]	2.575	1.384	1.069	2.460	4.505
beta1_pH[7,3]	2.517	0.434	1.690	2.510	3.372
beta1_pH[8,3]	2.744	0.351	2.079	2.739	3.446
beta1_pH[9,3]	2.920	0.572	2.118	2.820	4.440
beta1_pH[10,3]	2.953	0.501	2.160	2.889	4.136
beta1_pH[11,3]	2.719	0.401	1.957	2.712	3.513
beta1_pH[12,3]	4.043	0.443	3.217	4.011	4.983
beta1_pH[13,3]	1.728	0.347	1.084	1.720	2.414
beta1_pH[14,3]	2.490	0.348	1.812	2.491	3.178
beta1_pH[15,3]	1.968	0.337	1.359	1.963	2.668
beta1_pH[16,3]	1.790	0.325	1.143	1.792	2.418
beta2_pH[1,1]	0.463	0.116	0.282	0.448	0.730
beta2_pH[2,1]	0.570	0.282	0.250	0.517	1.203
beta2_pH[3,1]	0.648	0.473	0.226	0.549	1.664
beta2_pH[4,1]	0.467	0.209	0.202	0.432	0.928
beta2_pH[5,1]	1.494	1.030	0.248	1.364	3.946
beta2_pH[6,1]	0.184	0.065	0.088	0.174	0.337
beta2_pH[7,1]	0.012	0.091	0.000	0.000	0.068
beta2_pH[8,1]	0.239	0.088	0.123	0.224	0.451
beta2_pH[9,1]	0.427	0.202	0.176	0.389	0.911
beta2_pH[10,1]	0.616	0.257	0.286	0.565	1.253
beta2_pH[11,1]	0.781	0.210	0.470	0.748	1.284
beta2_pH[12,1]	1.376	0.509	0.741	1.266	2.590
beta2_pH[13,1]	0.744	0.231	0.409	0.704	1.291
beta2_pH[14,1]	0.839	0.212	0.533	0.807	1.330
beta2_pH[15,1]	0.816	0.291	0.410	0.761	1.543
beta2_pH[16,1]	0.363	0.166	0.160	0.321	0.817
beta2_pH[1,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[2,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[3,2]	-0.442	3.966	-8.156	-0.461	7.271
beta2_pH[4,2]	-0.395	3.951	-8.130	-0.433	7.507
beta2_pH[5,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[6,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[7,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[8,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[9,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[10,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[11,2]	-9.510	4.484	-20.897	-8.421	-3.828
beta2_pH[12,2]	-7.923	5.200	-21.089	-7.046	-0.955
beta2_pH[13,2]	-7.808	5.186	-20.951	-6.539	-1.661
beta2_pH[14,2]	-8.448	4.899	-21.017	-7.303	-2.473
beta2_pH[15,2]	-9.191	4.516	-20.754	-8.094	-3.634
beta2_pH[16,2]	-9.508	4.551	-21.468	-8.340	-3.960
beta2_pH[1,3]	0.000	0.003	0.000	0.000	0.002
beta2_pH[2,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[3,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[4,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[5,3]	7.754	5.929	-0.159	6.770	21.542
beta2_pH[6,3]	7.837	5.835	0.237	6.780	21.495
beta2_pH[7,3]	7.653	5.738	0.731	6.556	21.334
beta2_pH[8,3]	8.714	5.405	1.290	7.652	22.029
beta2_pH[9,3]	7.425	5.980	0.377	6.425	21.803
beta2_pH[10,3]	7.327	5.982	0.455	6.325	22.027
beta2_pH[11,3]	-2.610	2.646	-10.257	-1.822	-0.600
beta2_pH[12,3]	-2.773	2.493	-9.743	-1.982	-0.927
beta2_pH[13,3]	-3.115	2.755	-10.689	-2.210	-0.747
beta2_pH[14,3]	-3.107	2.648	-10.715	-2.267	-0.877
beta2_pH[15,3]	-3.281	2.709	-10.756	-2.356	-0.979
beta2_pH[16,3]	-3.305	2.847	-11.375	-2.341	-0.861
beta3_pH[1,1]	35.854	0.768	34.376	35.844	37.405
beta3_pH[2,1]	33.546	1.133	31.620	33.470	36.041
beta3_pH[3,1]	33.642	1.025	31.613	33.619	35.812
beta3_pH[4,1]	33.816	1.220	31.577	33.769	36.349
beta3_pH[5,1]	27.694	1.091	26.501	27.457	30.834
beta3_pH[6,1]	38.615	3.152	32.960	38.380	45.169
beta3_pH[7,1]	30.736	7.860	18.510	30.393	44.830
beta3_pH[8,1]	40.113	2.232	36.293	39.829	45.142
beta3_pH[9,1]	30.700	1.605	27.972	30.579	34.197
beta3_pH[10,1]	32.692	0.918	30.970	32.665	34.567
beta3_pH[11,1]	30.312	0.475	29.356	30.313	31.229
beta3_pH[12,1]	30.156	0.399	29.347	30.170	30.911
beta3_pH[13,1]	33.178	0.573	32.125	33.165	34.365
beta3_pH[14,1]	32.026	0.450	31.172	32.003	32.948
beta3_pH[15,1]	31.167	0.632	29.907	31.153	32.461
beta3_pH[16,1]	32.092	1.061	30.413	31.961	34.593
beta3_pH[1,2]	29.852	7.971	18.434	29.034	44.644
beta3_pH[2,2]	29.794	7.929	18.356	28.656	44.881
beta3_pH[3,2]	30.142	7.937	18.469	29.237	44.806
beta3_pH[4,2]	30.186	8.058	18.437	29.207	45.040
beta3_pH[5,2]	30.200	8.099	18.551	29.280	45.177
beta3_pH[6,2]	29.788	7.913	18.515	28.897	44.758
beta3_pH[7,2]	29.670	7.960	18.402	28.957	44.728
beta3_pH[8,2]	30.139	7.896	18.447	29.215	44.912
beta3_pH[9,2]	30.109	7.931	18.471	29.278	45.034
beta3_pH[10,2]	30.056	8.096	18.322	29.256	44.958
beta3_pH[11,2]	43.405	0.178	43.116	43.386	43.777
beta3_pH[12,2]	43.187	0.192	42.918	43.140	43.707
beta3_pH[13,2]	43.872	0.146	43.484	43.908	44.050
beta3_pH[14,2]	43.309	0.208	43.049	43.256	43.827
beta3_pH[15,2]	43.414	0.192	43.103	43.395	43.813
beta3_pH[16,2]	43.500	0.186	43.160	43.503	43.851
beta3_pH[1,3]	29.727	8.035	18.530	28.463	44.870
beta3_pH[2,3]	29.932	7.993	18.437	28.885	44.877
beta3_pH[3,3]	29.962	8.042	18.417	28.933	44.912
beta3_pH[4,3]	29.803	7.871	18.536	28.617	44.809
beta3_pH[5,3]	33.690	5.257	27.160	32.851	44.649
beta3_pH[6,3]	33.364	6.420	27.078	29.319	45.040
beta3_pH[7,3]	27.979	0.756	27.025	27.910	29.634
beta3_pH[8,3]	41.496	0.289	40.996	41.494	42.009
beta3_pH[9,3]	33.108	1.207	29.304	33.456	34.266
beta3_pH[10,3]	35.746	0.881	33.339	35.992	36.877
beta3_pH[11,3]	41.779	0.882	39.951	41.840	43.374
beta3_pH[12,3]	41.721	0.407	40.927	41.736	42.527
beta3_pH[13,3]	42.774	0.972	41.022	42.777	45.153
beta3_pH[14,3]	41.089	0.620	39.782	41.129	42.198
beta3_pH[15,3]	42.637	0.680	41.172	42.704	43.776
beta3_pH[16,3]	42.893	0.794	41.117	43.006	44.197
beta0_pelagic[1]	2.198	0.134	1.939	2.196	2.462
beta0_pelagic[2]	1.510	0.128	1.254	1.510	1.759
beta0_pelagic[3]	-1.219	1.946	-7.336	-0.552	0.544
beta0_pelagic[4]	-0.549	1.049	-3.379	-0.247	0.726
beta0_pelagic[5]	1.195	0.256	0.663	1.195	1.682
beta0_pelagic[6]	1.470	0.263	0.930	1.481	1.958
beta0_pelagic[7]	1.688	0.234	1.277	1.662	2.210
beta0_pelagic[8]	1.762	0.210	1.360	1.752	2.214
beta0_pelagic[9]	2.494	0.311	1.877	2.503	3.063
beta0_pelagic[10]	2.539	0.201	2.122	2.547	2.916
beta0_pelagic[11]	-0.012	0.543	-1.195	0.081	0.719
beta0_pelagic[12]	1.683	0.145	1.400	1.684	1.968
beta0_pelagic[13]	0.296	0.210	-0.171	0.316	0.648
beta0_pelagic[14]	-0.111	0.289	-0.779	-0.087	0.367
beta0_pelagic[15]	-0.269	0.142	-0.548	-0.266	0.003
beta0_pelagic[16]	0.253	0.317	-0.554	0.331	0.683
beta1_pelagic[1]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[2]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[3]	3.553	3.825	0.513	2.145	15.757
beta1_pelagic[4]	2.132	1.494	0.455	1.680	6.124
beta1_pelagic[5]	-0.077	0.312	-0.655	-0.084	0.539
beta1_pelagic[6]	-0.093	0.437	-0.821	-0.144	0.736
beta1_pelagic[7]	-0.007	0.349	-0.676	-0.011	0.661
beta1_pelagic[8]	-0.003	0.282	-0.571	0.000	0.553
beta1_pelagic[9]	0.187	0.485	-0.765	0.286	0.950
beta1_pelagic[10]	0.058	0.268	-0.466	0.052	0.581
beta1_pelagic[11]	3.822	1.221	2.156	3.655	6.387
beta1_pelagic[12]	2.783	0.319	2.190	2.772	3.429
beta1_pelagic[13]	3.001	0.758	1.771	2.896	4.688
beta1_pelagic[14]	4.415	1.065	2.821	4.241	6.853
beta1_pelagic[15]	2.928	0.272	2.402	2.924	3.475
beta1_pelagic[16]	3.740	1.045	2.684	3.353	6.596
beta2_pelagic[1]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[2]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[3]	1.386	5.661	0.012	0.114	18.738
beta2_pelagic[4]	2.369	6.709	0.021	0.329	26.389
beta2_pelagic[5]	-0.006	0.686	-1.438	-0.002	1.493
beta2_pelagic[6]	-0.092	0.680	-1.432	-0.131	1.305
beta2_pelagic[7]	-0.004	0.670	-1.388	0.005	1.318
beta2_pelagic[8]	-0.009	0.642	-1.341	-0.005	1.323
beta2_pelagic[9]	0.165	0.687	-1.299	0.233	1.562
beta2_pelagic[10]	0.029	0.634	-1.275	0.018	1.349
beta2_pelagic[11]	2.015	4.104	0.107	0.251	14.482
beta2_pelagic[12]	5.819	4.902	1.020	4.257	19.335
beta2_pelagic[13]	0.828	1.741	0.183	0.439	4.138
beta2_pelagic[14]	0.321	0.257	0.156	0.285	0.672
beta2_pelagic[15]	6.054	4.915	1.175	4.666	20.039
beta2_pelagic[16]	4.371	5.333	0.181	2.661	18.465
beta3_pelagic[1]	29.821	7.881	18.448	28.697	44.957
beta3_pelagic[2]	29.697	7.946	18.492	28.569	44.657
beta3_pelagic[3]	29.475	6.683	18.785	28.991	44.206
beta3_pelagic[4]	25.332	5.455	18.416	24.408	41.448
beta3_pelagic[5]	30.318	8.352	18.449	28.747	45.269
beta3_pelagic[6]	31.561	6.816	19.008	31.566	44.045
beta3_pelagic[7]	29.167	7.156	18.499	28.427	44.525
beta3_pelagic[8]	29.460	7.953	18.382	28.171	44.878
beta3_pelagic[9]	30.909	6.246	19.158	30.923	43.302
beta3_pelagic[10]	29.366	8.220	18.329	27.855	45.022
beta3_pelagic[11]	42.328	2.089	36.482	42.969	45.483
beta3_pelagic[12]	43.463	0.293	42.971	43.450	44.016
beta3_pelagic[13]	42.885	1.345	40.261	42.842	45.593
beta3_pelagic[14]	42.464	1.672	39.108	42.439	45.613
beta3_pelagic[15]	43.165	0.270	42.543	43.171	43.663
beta3_pelagic[16]	43.136	0.831	41.184	43.212	45.016
mu_beta0_pelagic[1]	0.469	1.236	-2.280	0.623	2.707
mu_beta0_pelagic[2]	1.826	0.389	1.011	1.830	2.560
mu_beta0_pelagic[3]	0.278	0.470	-0.725	0.310	1.164
tau_beta0_pelagic[1]	0.418	0.509	0.045	0.231	1.823
tau_beta0_pelagic[2]	2.698	2.588	0.260	1.973	9.974
tau_beta0_pelagic[3]	1.517	1.184	0.191	1.204	4.514
beta0_yellow[1]	-0.544	0.192	-0.989	-0.527	-0.233
beta0_yellow[2]	0.488	0.180	0.119	0.500	0.799
beta0_yellow[3]	-0.330	0.200	-0.763	-0.322	0.012
beta0_yellow[4]	0.787	0.347	-0.250	0.858	1.212
beta0_yellow[5]	-0.312	0.347	-0.986	-0.319	0.393
beta0_yellow[6]	1.134	0.167	0.814	1.133	1.454
beta0_yellow[7]	1.073	0.158	0.756	1.075	1.377
beta0_yellow[8]	1.017	0.154	0.716	1.020	1.321
beta0_yellow[9]	0.671	0.161	0.363	0.668	0.988
beta0_yellow[10]	0.580	0.141	0.310	0.578	0.866
beta0_yellow[11]	-1.986	0.452	-2.911	-1.979	-1.102
beta0_yellow[12]	-3.707	0.433	-4.593	-3.678	-2.911
beta0_yellow[13]	-3.716	0.471	-4.682	-3.683	-2.864
beta0_yellow[14]	-2.172	0.530	-3.150	-2.195	-1.020
beta0_yellow[15]	-2.878	0.427	-3.755	-2.863	-2.101
beta0_yellow[16]	-2.426	0.448	-3.308	-2.424	-1.543
beta1_yellow[1]	0.816	1.067	0.007	0.644	2.705
beta1_yellow[2]	1.110	0.462	0.598	1.037	2.180
beta1_yellow[3]	0.731	0.308	0.237	0.708	1.394
beta1_yellow[4]	1.505	0.920	0.656	1.220	4.312
beta1_yellow[5]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[6]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[7]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[8]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[9]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[10]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[11]	2.134	0.451	1.266	2.116	3.053
beta1_yellow[12]	2.503	0.450	1.680	2.480	3.428
beta1_yellow[13]	2.839	0.471	2.009	2.813	3.823
beta1_yellow[14]	2.244	0.528	1.109	2.259	3.284
beta1_yellow[15]	2.134	0.421	1.364	2.116	2.984
beta1_yellow[16]	2.188	0.449	1.305	2.184	3.102
beta2_yellow[1]	-3.206	2.734	-9.954	-2.516	-0.031
beta2_yellow[2]	-3.109	2.571	-9.590	-2.439	-0.150
beta2_yellow[3]	-2.993	2.598	-9.827	-2.271	-0.116
beta2_yellow[4]	-2.239	2.382	-8.374	-1.235	-0.077
beta2_yellow[5]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[6]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[7]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[8]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[9]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[10]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[11]	-4.535	2.784	-11.688	-3.835	-1.015
beta2_yellow[12]	-4.949	2.764	-12.028	-4.340	-1.354
beta2_yellow[13]	-4.799	2.679	-11.786	-4.093	-1.506
beta2_yellow[14]	-4.812	2.884	-11.929	-4.267	-0.665
beta2_yellow[15]	-4.323	2.750	-11.487	-3.667	-1.005
beta2_yellow[16]	-4.983	2.824	-12.152	-4.343	-1.374
beta3_yellow[1]	26.059	7.325	18.282	22.850	44.157
beta3_yellow[2]	29.021	1.970	24.235	28.904	32.759
beta3_yellow[3]	32.909	3.342	25.000	32.780	41.502
beta3_yellow[4]	29.063	3.843	20.642	28.209	36.309
beta3_yellow[5]	29.933	7.929	18.539	28.827	44.904
beta3_yellow[6]	29.981	7.882	18.437	29.178	44.842
beta3_yellow[7]	30.034	7.924	18.399	29.170	44.994
beta3_yellow[8]	30.337	7.977	18.425	29.382	44.928
beta3_yellow[9]	29.898	7.928	18.493	28.801	44.840
beta3_yellow[10]	30.297	7.820	18.591	29.625	45.113
beta3_yellow[11]	45.291	0.591	44.023	45.399	45.969
beta3_yellow[12]	43.314	0.382	42.565	43.284	44.050
beta3_yellow[13]	44.861	0.399	43.977	44.929	45.559
beta3_yellow[14]	44.199	1.336	42.919	44.288	45.855
beta3_yellow[15]	45.188	0.537	44.170	45.174	45.972
beta3_yellow[16]	44.581	0.644	43.413	44.565	45.810
mu_beta0_yellow[1]	0.087	0.571	-1.107	0.093	1.295
mu_beta0_yellow[2]	0.650	0.359	-0.118	0.668	1.303
mu_beta0_yellow[3]	-2.468	0.617	-3.509	-2.546	-0.992
tau_beta0_yellow[1]	1.872	2.947	0.096	1.122	7.640
tau_beta0_yellow[2]	3.086	3.546	0.285	2.126	11.779
tau_beta0_yellow[3]	1.580	3.116	0.111	0.924	6.472
beta0_black[1]	-0.076	0.158	-0.384	-0.077	0.241
beta0_black[2]	1.913	0.130	1.663	1.914	2.171
beta0_black[3]	1.317	0.135	1.063	1.318	1.581
beta0_black[4]	2.427	0.135	2.156	2.431	2.685
beta0_black[5]	1.603	2.097	-3.098	1.679	5.679
beta0_black[6]	1.518	1.999	-3.100	1.623	5.446
beta0_black[7]	1.591	2.006	-3.019	1.667	5.690
beta0_black[8]	1.296	0.231	0.848	1.298	1.748
beta0_black[9]	2.452	0.249	1.963	2.450	2.943
beta0_black[10]	1.477	0.134	1.215	1.476	1.743
beta0_black[11]	3.481	0.155	3.173	3.483	3.773
beta0_black[12]	4.865	0.178	4.518	4.861	5.223
beta0_black[13]	-0.161	0.349	-0.847	-0.131	0.349
beta0_black[14]	2.855	0.161	2.541	2.850	3.178
beta0_black[15]	1.297	0.156	0.988	1.298	1.593
beta0_black[16]	4.268	0.164	3.942	4.267	4.596
beta2_black[1]	8.038	10.197	0.531	3.485	39.190
beta2_black[2]	0.000	0.000	0.000	0.000	0.000
beta2_black[3]	0.000	0.000	0.000	0.000	0.000
beta2_black[4]	0.000	0.000	0.000	0.000	0.000
beta2_black[5]	0.000	0.000	0.000	0.000	0.000
beta2_black[6]	0.000	0.000	0.000	0.000	0.000
beta2_black[7]	0.000	0.000	0.000	0.000	0.000
beta2_black[8]	0.000	0.000	0.000	0.000	0.000
beta2_black[9]	0.000	0.000	0.000	0.000	0.000
beta2_black[10]	0.000	0.000	0.000	0.000	0.000
beta2_black[11]	0.000	0.000	0.000	0.000	0.000
beta2_black[12]	0.000	0.000	0.000	0.000	0.000
beta2_black[13]	-1.848	1.640	-6.180	-1.320	-0.214
beta2_black[14]	0.000	0.000	0.000	0.000	0.000
beta2_black[15]	0.000	0.000	0.000	0.000	0.000
beta2_black[16]	0.000	0.000	0.000	0.000	0.000
beta3_black[1]	41.784	1.129	39.885	41.964	43.317
beta3_black[2]	25.000	0.000	25.000	25.000	25.000
beta3_black[3]	25.000	0.000	25.000	25.000	25.000
beta3_black[4]	25.000	0.000	25.000	25.000	25.000
beta3_black[5]	25.000	0.000	25.000	25.000	25.000
beta3_black[6]	25.000	0.000	25.000	25.000	25.000
beta3_black[7]	25.000	0.000	25.000	25.000	25.000
beta3_black[8]	25.000	0.000	25.000	25.000	25.000
beta3_black[9]	25.000	0.000	25.000	25.000	25.000
beta3_black[10]	25.000	0.000	25.000	25.000	25.000
beta3_black[11]	25.000	0.000	25.000	25.000	25.000
beta3_black[12]	25.000	0.000	25.000	25.000	25.000
beta3_black[13]	39.041	1.796	36.566	39.299	40.647
beta3_black[14]	25.000	0.000	25.000	25.000	25.000
beta3_black[15]	25.000	0.000	25.000	25.000	25.000
beta3_black[16]	25.000	0.000	25.000	25.000	25.000
beta4_black[1]	-0.262	0.196	-0.640	-0.258	0.114
beta4_black[2]	0.246	0.182	-0.107	0.248	0.605
beta4_black[3]	-0.935	0.194	-1.307	-0.936	-0.551
beta4_black[4]	0.434	0.219	0.018	0.433	0.894
beta4_black[5]	0.164	2.448	-4.316	0.116	4.677
beta4_black[6]	0.238	2.465	-4.352	0.130	4.975
beta4_black[7]	0.220	2.372	-4.338	0.144	4.952
beta4_black[8]	-0.687	0.375	-1.432	-0.685	0.024
beta4_black[9]	1.468	1.051	-0.177	1.335	3.754
beta4_black[10]	0.026	0.187	-0.353	0.029	0.392
beta4_black[11]	-0.690	0.217	-1.128	-0.692	-0.251
beta4_black[12]	0.176	0.321	-0.449	0.171	0.838
beta4_black[13]	-1.188	0.228	-1.640	-1.182	-0.756
beta4_black[14]	-0.183	0.244	-0.649	-0.191	0.297
beta4_black[15]	-0.894	0.212	-1.306	-0.893	-0.483
beta4_black[16]	-0.592	0.231	-1.044	-0.593	-0.142
mu_beta0_black[1]	1.254	0.924	-0.699	1.316	2.967
mu_beta0_black[2]	1.571	0.912	-0.677	1.652	3.291
mu_beta0_black[3]	2.515	0.970	0.459	2.564	4.301
tau_beta0_black[1]	0.645	0.611	0.058	0.453	2.223
tau_beta0_black[2]	1.848	3.429	0.052	0.844	9.350
tau_beta0_black[3]	0.237	0.155	0.050	0.201	0.632
beta0_dsr[11]	-2.893	0.294	-3.477	-2.894	-2.305
beta0_dsr[12]	4.550	0.281	4.014	4.550	5.097
beta0_dsr[13]	-1.356	0.341	-1.998	-1.336	-0.783
beta0_dsr[14]	-3.654	0.519	-4.709	-3.634	-2.675
beta0_dsr[15]	-1.938	0.281	-2.485	-1.941	-1.405
beta0_dsr[16]	-2.993	0.366	-3.726	-2.986	-2.287
beta1_dsr[11]	4.825	0.308	4.229	4.822	5.425
beta1_dsr[12]	7.243	18.080	2.240	5.044	20.369
beta1_dsr[13]	2.869	0.407	2.258	2.842	3.546
beta1_dsr[14]	6.320	0.544	5.283	6.306	7.441
beta1_dsr[15]	3.333	0.291	2.769	3.332	3.894
beta1_dsr[16]	5.814	0.386	5.081	5.814	6.577
beta2_dsr[11]	-8.237	2.384	-14.053	-7.913	-4.623
beta2_dsr[12]	-7.021	2.624	-12.751	-6.836	-2.282
beta2_dsr[13]	-6.517	2.733	-12.273	-6.427	-1.274
beta2_dsr[14]	-6.205	2.619	-11.665	-6.130	-1.785
beta2_dsr[15]	-7.744	2.409	-13.294	-7.453	-3.963
beta2_dsr[16]	-7.904	2.370	-13.487	-7.575	-4.130
beta3_dsr[11]	43.486	0.149	43.208	43.484	43.777
beta3_dsr[12]	33.966	0.833	32.031	34.134	34.815
beta3_dsr[13]	43.244	0.426	42.757	43.194	43.881
beta3_dsr[14]	43.346	0.238	43.072	43.275	43.959
beta3_dsr[15]	43.508	0.190	43.161	43.510	43.856
beta3_dsr[16]	43.438	0.157	43.172	43.423	43.758
beta4_dsr[11]	0.589	0.221	0.164	0.591	1.012
beta4_dsr[12]	0.241	0.443	-0.635	0.245	1.121
beta4_dsr[13]	-0.166	0.224	-0.614	-0.167	0.267
beta4_dsr[14]	0.149	0.254	-0.348	0.153	0.635
beta4_dsr[15]	0.723	0.212	0.324	0.722	1.159
beta4_dsr[16]	0.151	0.232	-0.316	0.151	0.600
beta0_slope[11]	-1.851	0.148	-2.138	-1.853	-1.555
beta0_slope[12]	-4.471	0.253	-4.981	-4.471	-3.985
beta0_slope[13]	-1.358	0.204	-1.869	-1.339	-1.039
beta0_slope[14]	-2.674	0.168	-2.999	-2.676	-2.343
beta0_slope[15]	-1.349	0.148	-1.635	-1.351	-1.048
beta0_slope[16]	-2.738	0.158	-3.048	-2.738	-2.430
beta1_slope[11]	4.489	0.223	4.047	4.491	4.937
beta1_slope[12]	3.989	0.458	3.047	3.998	4.909
beta1_slope[13]	2.766	0.532	2.183	2.663	4.532
beta1_slope[14]	6.318	0.416	5.521	6.309	7.163
beta1_slope[15]	3.009	0.203	2.622	3.011	3.410
beta1_slope[16]	5.281	0.285	4.717	5.283	5.842
beta2_slope[11]	8.553	2.276	5.042	8.225	13.843
beta2_slope[12]	6.605	2.961	1.170	6.588	12.828
beta2_slope[13]	5.100	3.033	0.322	5.014	11.438
beta2_slope[14]	6.296	2.513	2.247	6.100	11.841
beta2_slope[15]	8.195	2.401	4.393	7.832	13.619
beta2_slope[16]	7.733	2.343	4.174	7.379	13.182
beta3_slope[11]	43.459	0.131	43.229	43.450	43.729
beta3_slope[12]	43.356	0.287	42.895	43.313	43.945
beta3_slope[13]	43.465	0.412	42.894	43.406	44.250
beta3_slope[14]	43.273	0.138	43.095	43.242	43.620
beta3_slope[15]	43.489	0.157	43.198	43.488	43.786
beta3_slope[16]	43.373	0.145	43.150	43.351	43.714
beta4_slope[11]	-0.727	0.164	-1.059	-0.725	-0.411
beta4_slope[12]	-1.168	0.474	-2.168	-1.123	-0.381
beta4_slope[13]	0.089	0.165	-0.226	0.087	0.411
beta4_slope[14]	-0.095	0.200	-0.476	-0.095	0.300
beta4_slope[15]	-0.762	0.160	-1.076	-0.762	-0.454
beta4_slope[16]	-0.162	0.176	-0.511	-0.161	0.167
sigma_H[1]	0.193	0.053	0.096	0.190	0.306
sigma_H[2]	0.171	0.031	0.119	0.168	0.236
sigma_H[3]	0.196	0.042	0.121	0.194	0.289
sigma_H[4]	0.423	0.079	0.297	0.413	0.607
sigma_H[5]	0.999	0.208	0.611	0.991	1.428
sigma_H[6]	0.390	0.199	0.034	0.384	0.808
sigma_H[7]	0.316	0.067	0.214	0.305	0.478
sigma_H[8]	0.414	0.090	0.279	0.404	0.613
sigma_H[9]	0.527	0.128	0.329	0.512	0.829
sigma_H[10]	0.216	0.043	0.138	0.213	0.308
sigma_H[11]	0.278	0.046	0.200	0.275	0.378
sigma_H[12]	0.435	0.165	0.205	0.409	0.770
sigma_H[13]	0.215	0.038	0.152	0.211	0.299
sigma_H[14]	0.510	0.090	0.358	0.504	0.704
sigma_H[15]	0.246	0.040	0.178	0.243	0.335
sigma_H[16]	0.224	0.044	0.154	0.220	0.323
lambda_H[1]	2.846	3.569	0.152	1.596	12.368
lambda_H[2]	7.915	7.224	0.794	5.776	28.314
lambda_H[3]	6.397	10.008	0.267	3.073	33.788
lambda_H[4]	0.006	0.004	0.001	0.005	0.018
lambda_H[5]	4.325	9.610	0.031	1.093	31.788
lambda_H[6]	7.537	14.361	0.009	1.127	49.876
lambda_H[7]	0.011	0.008	0.002	0.009	0.032
lambda_H[8]	8.614	11.268	0.126	4.796	37.624
lambda_H[9]	0.015	0.010	0.003	0.013	0.040
lambda_H[10]	0.314	0.673	0.030	0.200	1.104
lambda_H[11]	0.259	0.386	0.011	0.126	1.236
lambda_H[12]	4.703	5.779	0.176	2.659	21.903
lambda_H[13]	3.468	3.003	0.255	2.659	11.446
lambda_H[14]	3.177	3.850	0.222	2.007	13.111
lambda_H[15]	0.025	0.033	0.003	0.017	0.098
lambda_H[16]	0.777	1.150	0.037	0.400	3.636
mu_lambda_H[1]	4.325	1.903	1.213	4.155	8.456
mu_lambda_H[2]	3.844	1.945	0.656	3.686	7.917
mu_lambda_H[3]	3.500	1.848	0.811	3.216	7.800
sigma_lambda_H[1]	8.601	4.297	2.110	7.985	18.035
sigma_lambda_H[2]	8.401	4.661	1.121	7.889	18.168
sigma_lambda_H[3]	6.212	3.920	1.067	5.418	16.109
beta_H[1,1]	6.812	1.085	4.240	6.994	8.452
beta_H[2,1]	9.869	0.494	8.771	9.904	10.733
beta_H[3,1]	7.984	0.788	6.069	8.112	9.233
beta_H[4,1]	9.350	7.778	-7.192	9.573	24.675
beta_H[5,1]	0.146	2.304	-4.623	0.298	4.097
beta_H[6,1]	3.173	3.894	-6.846	4.533	7.639
beta_H[7,1]	-0.512	6.175	-14.056	-0.009	10.271
beta_H[8,1]	1.278	3.064	-2.209	1.241	3.434
beta_H[9,1]	12.948	5.799	1.493	12.918	24.483
beta_H[10,1]	7.072	1.675	3.618	7.151	10.290
beta_H[11,1]	5.058	3.562	-2.907	5.807	9.970
beta_H[12,1]	2.619	1.043	0.772	2.537	4.970
beta_H[13,1]	9.057	0.907	7.163	9.129	10.490
beta_H[14,1]	2.166	1.071	0.037	2.173	4.157
beta_H[15,1]	-6.104	3.830	-12.953	-6.179	2.238
beta_H[16,1]	3.576	2.755	-0.885	3.258	10.021
beta_H[1,2]	7.899	0.243	7.398	7.901	8.359
beta_H[2,2]	10.024	0.134	9.763	10.023	10.289
beta_H[3,2]	8.949	0.200	8.563	8.946	9.350
beta_H[4,2]	3.599	1.466	0.822	3.544	6.556
beta_H[5,2]	1.937	0.932	0.083	1.952	3.678
beta_H[6,2]	5.750	1.025	3.306	5.925	7.308
beta_H[7,2]	2.950	1.141	0.936	2.874	5.416
beta_H[8,2]	3.033	0.968	1.478	3.149	4.242
beta_H[9,2]	3.522	1.128	1.317	3.503	5.860
beta_H[10,2]	8.205	0.339	7.477	8.213	8.875
beta_H[11,2]	9.778	0.642	8.842	9.668	11.201
beta_H[12,2]	3.940	0.366	3.241	3.933	4.692
beta_H[13,2]	9.123	0.252	8.650	9.113	9.641
beta_H[14,2]	4.029	0.353	3.354	4.022	4.724
beta_H[15,2]	11.359	0.683	9.890	11.399	12.618
beta_H[16,2]	4.550	0.831	2.942	4.521	6.199
beta_H[1,3]	8.501	0.236	8.067	8.485	8.998
beta_H[2,3]	10.066	0.121	9.825	10.065	10.304
beta_H[3,3]	9.623	0.168	9.302	9.621	9.968
beta_H[4,3]	-2.533	0.888	-4.240	-2.540	-0.764
beta_H[5,3]	3.795	0.603	2.495	3.825	4.898
beta_H[6,3]	8.007	1.194	6.401	7.620	10.579
beta_H[7,3]	-3.077	0.663	-4.435	-3.079	-1.837
beta_H[8,3]	5.235	0.466	4.633	5.173	6.213
beta_H[9,3]	-2.858	0.727	-4.323	-2.853	-1.416
beta_H[10,3]	8.677	0.275	8.145	8.683	9.217
beta_H[11,3]	8.535	0.289	7.906	8.560	9.034
beta_H[12,3]	5.249	0.318	4.519	5.293	5.771
beta_H[13,3]	8.841	0.178	8.491	8.846	9.186
beta_H[14,3]	5.713	0.282	5.128	5.733	6.200
beta_H[15,3]	10.367	0.321	9.741	10.362	11.014
beta_H[16,3]	6.196	0.617	4.873	6.267	7.218
beta_H[1,4]	8.269	0.173	7.892	8.281	8.578
beta_H[2,4]	10.126	0.123	9.846	10.135	10.337
beta_H[3,4]	10.114	0.167	9.740	10.132	10.400
beta_H[4,4]	11.800	0.455	10.855	11.818	12.656
beta_H[5,4]	5.470	0.758	4.254	5.373	7.218
beta_H[6,4]	7.076	0.931	4.983	7.360	8.323
beta_H[7,4]	8.312	0.347	7.621	8.315	8.986
beta_H[8,4]	6.707	0.233	6.268	6.714	7.103
beta_H[9,4]	7.224	0.460	6.345	7.221	8.141
beta_H[10,4]	7.754	0.235	7.318	7.742	8.235
beta_H[11,4]	9.385	0.202	8.987	9.389	9.777
beta_H[12,4]	7.148	0.220	6.729	7.140	7.613
beta_H[13,4]	9.043	0.141	8.766	9.047	9.304
beta_H[14,4]	7.742	0.223	7.302	7.739	8.195
beta_H[15,4]	9.464	0.237	8.990	9.461	9.932
beta_H[16,4]	9.360	0.239	8.925	9.351	9.857
beta_H[1,5]	8.976	0.141	8.680	8.979	9.250
beta_H[2,5]	10.782	0.095	10.603	10.781	10.976
beta_H[3,5]	10.921	0.176	10.600	10.909	11.284
beta_H[4,5]	8.380	0.469	7.494	8.365	9.360
beta_H[5,5]	5.423	0.573	4.122	5.467	6.420
beta_H[6,5]	8.807	0.630	7.931	8.643	10.316
beta_H[7,5]	6.747	0.337	6.096	6.736	7.452
beta_H[8,5]	8.212	0.203	7.858	8.201	8.616
beta_H[9,5]	8.203	0.477	7.240	8.204	9.116
beta_H[10,5]	10.083	0.231	9.628	10.089	10.530
beta_H[11,5]	11.511	0.227	11.070	11.505	11.963
beta_H[12,5]	8.479	0.200	8.079	8.478	8.855
beta_H[13,5]	10.012	0.133	9.760	10.014	10.280
beta_H[14,5]	9.201	0.229	8.774	9.188	9.694
beta_H[15,5]	11.172	0.253	10.661	11.178	11.653
beta_H[16,5]	9.913	0.178	9.536	9.919	10.242
beta_H[1,6]	10.184	0.189	9.847	10.169	10.598
beta_H[2,6]	11.515	0.107	11.301	11.516	11.723
beta_H[3,6]	10.810	0.164	10.452	10.821	11.117
beta_H[4,6]	12.887	0.828	11.213	12.912	14.417
beta_H[5,6]	5.894	0.611	4.707	5.880	7.128
beta_H[6,6]	8.776	0.682	6.999	8.904	9.766
beta_H[7,6]	9.888	0.577	8.749	9.902	11.019
beta_H[8,6]	9.521	0.268	9.031	9.540	9.977
beta_H[9,6]	8.470	0.802	6.940	8.444	10.069
beta_H[10,6]	9.513	0.322	8.812	9.533	10.083
beta_H[11,6]	10.806	0.347	10.050	10.832	11.425
beta_H[12,6]	9.379	0.251	8.909	9.364	9.909
beta_H[13,6]	11.044	0.164	10.745	11.033	11.376
beta_H[14,6]	9.819	0.295	9.227	9.831	10.391
beta_H[15,6]	10.826	0.429	10.006	10.828	11.686
beta_H[16,6]	10.537	0.241	10.043	10.542	11.007
beta_H[1,7]	10.825	0.903	8.672	10.947	12.277
beta_H[2,7]	12.215	0.420	11.352	12.221	13.042
beta_H[3,7]	10.557	0.690	8.962	10.636	11.709
beta_H[4,7]	2.494	4.245	-5.586	2.369	11.062
beta_H[5,7]	6.370	1.823	2.934	6.354	10.334
beta_H[6,7]	9.645	2.451	4.584	9.584	15.755
beta_H[7,7]	10.427	2.912	4.768	10.373	16.309
beta_H[8,7]	10.927	0.960	9.400	10.904	12.651
beta_H[9,7]	4.444	4.055	-3.934	4.511	12.330
beta_H[10,7]	9.835	1.484	7.153	9.737	13.122
beta_H[11,7]	10.984	1.691	7.824	10.896	14.713
beta_H[12,7]	10.005	0.934	7.916	10.074	11.553
beta_H[13,7]	11.673	0.739	10.001	11.771	12.838
beta_H[14,7]	10.400	0.979	8.354	10.429	12.135
beta_H[15,7]	12.053	2.232	7.595	12.101	16.349
beta_H[16,7]	12.292	1.280	10.038	12.175	15.192
beta0_H[1]	8.565	12.945	-18.229	8.562	35.427
beta0_H[2]	10.627	6.516	-1.914	10.571	23.862
beta0_H[3]	9.416	9.605	-11.760	9.571	28.104
beta0_H[4]	10.074	183.623	-364.794	8.282	377.320
beta0_H[5]	4.098	23.863	-44.109	4.209	52.428
beta0_H[6]	7.274	50.687	-98.636	7.926	114.717
beta0_H[7]	0.006	143.380	-294.450	0.529	299.519
beta0_H[8]	6.308	22.192	-17.240	6.284	28.087
beta0_H[9]	9.103	119.760	-238.832	8.227	243.300
beta0_H[10]	8.265	33.042	-56.717	8.373	74.100
beta0_H[11]	8.462	52.756	-94.696	8.937	113.891
beta0_H[12]	6.043	11.399	-18.003	6.568	28.354
beta0_H[13]	9.947	11.289	-11.687	9.996	30.291
beta0_H[14]	7.167	11.623	-15.885	6.984	30.868
beta0_H[15]	7.754	109.876	-209.463	7.687	236.625
beta0_H[16]	8.363	28.347	-45.867	8.091	63.858